79. The difference in the distances of the location of the explosion from A and B is given: 600 m. Therefore, the location of the explosion is restricted to points on a hyperbola, the length of whose transverse axis is 600 m. Equation: ${\displaystyle \frac{x^2}{90\text{,}000}}-{\displaystyle \frac{y^2}{160\text{,}000}}=1$

81. Let the coordinates of Nicole be $(-4000,0)$ and those of Juan be $(4000,0).$

83. Let the coordinates of A be $(-150,0)$ and the coordinates of B be (15, 0) Equation: ${\displaystyle \frac{x^2}{5625}}-{\displaystyle \frac{y^2}{16,875}}=1$

85. Let the coordinates of A be $(-125,0)$ and the coordinates of B be (125, 0). The plane is flying on the line $y=50$. At the time of receiving the signals, the plane is at $(50.5238\text{,}50)$.

87. Possible locations of the boat: $(-1397.427,1225.2945),(-281.3655,209.9383),$ (359.5894, 288.219), (1059.7444, 925.19691)